what is the difference between a moral obligation and a moral duty?

[Free Trade is managed by the invisible hand.]

just wondering.

[Bo]

Obligation--Forced to do someting
Duty--Supposed to do something, but not forced to

[anvi]

Right. 

If Kant were answering this question, he would say that an obligation is imposed on you by social norms, and the motivation to adhere to the norn is a sure sign of heteronomy, or that one is compelled to do things for non-rational reasons.

A moral duty on the other hand is arrived at by oneself, through a reflective process that determines what one must do by finding the applicable categorical imperative.  People who can rationally determine their duty and be motivated by it and not any external compulsions are expressing their true rational nature, and are thus autonomous, or free.

[Swing low, sweet chariot. Comin' for to carry me home.]

Right. 

If Kant were answering this question, he would say that an obligation is imposed on you by social norms, and the motivation to adhere to the norn is a sure sign of heteronomy, or that one is compelled to do things for non-rational reasons.

A moral duty on the other hand is arrived at by oneself, through a reflective process that determines what one must do by finding the applicable categorical imperative.  People who can rationally determine their duty and be motivated by it and not any external compulsions are expressing their true rational nature, and are thus autonomous, or free.

in the bible, they are mostly synonyms

Rom 8:12 "Therefore, brothers, we have an obligation—but it is not to the sinful nature, to live according to it."

this was not an obligation due to "non-rational reasons", rather is the conclusion of a rational train of thought.

Ecc 12:13 "Let us hear the conclusion of the whole matter: Fear God, and keep his commandments: for this is the whole duty of man."

Obviously, this duty is NOT "arrived at by oneself, through a reflective process that determines what one must do by finding the applicable categorical imperative", rather the duty is handed down by God.

[anvi]

Yes, I think in a Biblical context, there would not be much point distinguishing between a moral obligation and a moral duty, since both orgininate in God's commandments for human conduct. 

There are also many philosophers who would not make any distinction between obligation and duty.  Kant is one of the only major Western philosophers who does, and I was just describing the distinction he made.